Chajda, I., & Länger, H. (2022, August 29). Filters and congruences in sectionally pseudocomplemented lattices and posets [Conference Presentation]. Summer School on General Algebra and Ordered Sets 2022, Hotel Sorea Titris, Tatranská Lomnica, Vysoké Tatry, Slovakia.
E104 - Institut für Diskrete Mathematik und Geometrie
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Date (published):
29-Aug-2022
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Event name:
Summer School on General Algebra and Ordered Sets 2022
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Event date:
28-Aug-2022 - 2-Sep-2022
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Event place:
Hotel Sorea Titris, Tatranská Lomnica, Vysoké Tatry, Slovakia
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Keywords:
Sectionally pseudocomplemented lattice, sectionally pseudocomplemented poset, filter, congruence, weak regularity, congruence permutability, Maltsev term, ideal term, closedness of a subset, congruence class, deductive system, partial term
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Abstract:
Together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented lattices - these structures can serve as an algebraic semantics of certain intuitionistic logics. The aim of the present paper is to define congruences and filters in these structures, derive mutual relationships between them and describe basic properties of congruences in strongly sectionally pseudocomplemented posets. For the description of filters both in sectionally pseudocomplemented lattices and posets, we use the tools introduced by A. Ursini, i.e. ideal terms and the closedness with respect to them. It seems to be of some interest that a similar machinery can be applied also for strongly sectionally pseudocomplemented posets in spite of the fact that the corresponding ideal terms are not everywhere defined.
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Project (external):
Austrian Science Fund Czech Science Foundation OeAD-GmbH IGA